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A Posteriori Error Analysis of Hybrid High-Order Methods for the Elliptic Obstacle Problem

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Abstract

In this article, a posteriori error analysis of the elliptic obstacle problem is addressed using hybrid high-order methods. The method involve cell unknowns represented by degree-r polynomials and face unknowns represented by degree-s polynomials, where \(r=0\) and s is either 0 or 1. The discrete obstacle constraints are specifically applied to the cell unknowns. The analysis hinges on the construction of a suitable Lagrange multiplier, a residual functional and a linear averaging map. The reliability and the efficiency of the proposed a posteriori error estimator is discussed, and the study is concluded by numerical experiments supporting the theoretical results.

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The second author’s work is supported by IIT Delhi institute fellowship.

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Correspondence to Ritesh Singla.

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Porwal, K., Singla, R. A Posteriori Error Analysis of Hybrid High-Order Methods for the Elliptic Obstacle Problem. J Sci Comput 102, 15 (2025). https://doi.org/10.1007/s10915-024-02744-6

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